Measured before inflation, interest rates have never been so low in so much of the world.

On July 5, the day after the U.S.’s 240th birthday, the yield on 10-year Treasury debt fell below 1.4% for the first time in the nation’s history.

World-wide, $13 trillion in debt is yielding less than zero; in “normal” times, when those bonds might have yielded 3% or so, investors would have earned roughly $400 billion on them annually. Now, investors are spending, rather than earning, tens of billions of dollars a year to hold those bonds—much as you might pay a storage company to keep your heirlooms safe for you.

However, this is far from the first time that interest rates have gone negative—once you account for inflation to measure what economists call “real” rates. Adjusted for changes in the cost of living, the yield on Treasury bills was negative in 18 out of the 27 years between 1933 and 1959. Over the same period, intermediate-term Treasurys had negative real yields in nine years. In the 1940s and again in the 1970s, negative real rates were common world-wide.

Nor is this the first time stocks have hit records amid negative rates. In 1958, short-term Treasury bills yielded minus 0.2% after inflation. Stocks nevertheless rose 43.4% that year to reach what then were all-time highs.

None of this means there is nothing to worry about. Returns on stocks and bonds are almost certain to shrink, and investors all around you are likely to take reckless risks as they become increasingly desperate for income. In a world turned upside down, sanity will be your most valuable asset as an investor.

Today’s yield drought is “unprecedented in our lives and limited experience, but it’s not at all unprecedented in history,” says Thomas Coleman, a former hedge-fund manager who runs the Center for Economic Policy at the University of Chicago’s Harris School of Public Policy. “What’s fundamentally different now is that we have negative real rates without high and unexpected inflation.”

In other words, earning nothing on your bonds isn’t the result of sudden shocks from inflation, as it was in the 1970s. It is the deliberate result of central-bank policies that have failed to produce inflation.

Banks (and governments) in Europe and Asia have kept lending to delinquent debtors in order to avoid marking down the value of their bad loans. That has kept the banks from extending credit to worthwhile borrowers. So the European Central Bank and the Bank of Japan have sharply cut interest rates to “try taxing the banks in a way that induces them to hold less cash and to lend more,” says Carmen Reinhart, an economist at the John F. Kennedy School of Government at Harvard University. Until lenders finally write down the value of their bad debt, she says, the “financial repression” of low interest rates will keep transferring massive amounts of wealth from savers to borrowers.

Rates probably won’t rise until almost no one on earth is expecting them to. When that happens, it will hurt.

Nevertheless, even at today’s emaciated yields, bonds remain a powerful hedge against declines in the stock market, says Fran Kinniry, an investment strategist at Vanguard Group.

Treasury bonds rose 1% on June 24, when the British vote to exit the European Union knocked U.S. stocks down almost 4%.

With such slim prospective returns on offer, you will have to lower your expectations and raise the amount you save.

“Investing is always a partnership between you and the markets,” Mr. Kinniry says. In the 1980s and 1990s, when stocks and bonds alike racked up double-digit average returns, the markets did most of the work. “But now you are going to have to be the majority partner,” he says.

In this weird world, if you want to have more money, you will need to save a lot more money.